Due to the wide existence and large morphological variances of nuclei, accurate nuclei instance segmentation is still one of the most challenging tasks in computational pathology. The annotating of nuclei instances, requiring experienced pathologists to manually draw the contours, is extremely laborious and expensive, which often results in the deficiency of annotated data. The deep learning based segmentation approaches, which highly rely on the quantity of training data, are difficult to fully demonstrate their capacity in this area. In this paper, we propose a novel self-supervised learning framework to deeply exploit the capacity of widely-used convolutional neural networks (CNNs) on the nuclei instance segmentation task. The proposed approach involves two sub-tasks (i.e., scale-wise triplet learning and count ranking), which enable neural networks to implicitly leverage the prior-knowledge of nuclei size and quantity, and accordingly mine the instance-aware feature representations from the raw data. Experimental results on the publicly available MoNuSeg dataset show that the proposed self-supervised learning approach can remarkably boost the segmentation accuracy of nuclei instance—a new state-of-the-art average Aggregated Jaccard Index (AJI) of 70.63%, is achieved by our self-supervised ResUNet-101. To our best knowledge, this is the first work focusing on the self-supervised learning for instance segmentation.